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Dynamical magnetic excitations with spin-orbit interaction in realistic nanostructures

Periodic Reporting for period 4 - Dynasore (Dynamical magnetic excitations with spin-orbit interaction in realistic nanostructures)

Reporting period: 2020-12-01 to 2021-05-31

Magnetism is at the heart of information technology. Most of the information stored worldwide is based on concepts involving the spin that an electron can carry. Today, we are producing more and more information that we want to store and access in smaller devices at shorter time scales than currently available. This calls for paradigm shifts not only in what defines the information-bit but also in the concepts used to read and write information. The goal of this project is to explore how fundamental electron's degrees of freedom - spin, charge and spin-orbit interaction - give rise to new magnetic states of matter, how they can be manipulated efficiently and how they behave over time once they are shaked with external stimuli. Utilising fundamental concepts derived from quantum mechanics, we aim at exploring, realistically, new magnetic phases of matter and their corresponding dynamical excited states using, in particular, atomic design to tailor beneficial physical properties down to the atomic level.

We propose to go beyond the state of the art by investigating from first-principles the dynamical properties of chiral spin textures in nanostructures from 2-dimensions to 0-dimension with these nanostructures being deposited on different substrates where spin-orbit interaction plays a major role. Understanding their response to external dynamical fields (electric/magnetic) or currents will impact on the burgeoning field of nano-spin-orbitronics. Indeed, to achieve efficient manipulation of nano-sized functional spin textures, it is imperative to exploit and understand their resonant motion, analogous to the role of ferromagnetic resonance in spintronics. A magnetic skyrmion is an example of a spin-swirling texture characterized by a topological number that will be explored. This spin state has huge potential in nanotechnologies thanks to the low spin currents needed to manipulate it.

Based on time-dependent density functional theory and many-body perturbation theory, our innovative scheme will deliver a paradigm shift with respect to existing theoretical methodologies and will provide a fundamental understanding of: (i) the occurrence of chiral spin textures in reduced dimensions, (ii) their dynamical spin-excitation spectra and the coupling of the different excitation degrees of freedom and (iii) their impact on the electronic structure.

We expect that the results collected from this project will contribute to a better understanding on how to realise nano-devices of importance in nanotechnologies and to discover effects that can be useful in storing, manipulating and reading information.
We made good progress in the realization of our objectives. We made unexpected discoveries that pushed us to investigate novel interesting effects. We developed several softwares dealing with spin-orbit driven physics, non-collinear magnetism and dynamical spin-effects, which allowed us to harvest valuable knowledge essential in the field of spin-orbitronics. We successfully made progress in producing a software for dynamical spin-excitations for the treatment of longitudinal spin-excitations of nanostructures on surfaces. We designed a method for accessing zero-point quantum fluctuations. The tensor of dynamical magnetic susceptibility including the spin-orbit interactions is now accessible and we managed to build the corresponding self-energy describing the interaction of electrons and spin-excitations. We developed a new software called TiTan devoted to the calculations of dynamical susceptibility and dynamical transport properties in extended/periodic materials. Moreover, we succeeded in simulating from first-principles complex spin-textures containing a thousand of magnetic atoms.

We introduced a new family of chiral magnetic interactions involving multi-spins beyond the usual bilinear Dzyaloashinskii-Moriya interactions (DMI's). The mechanism leading to multi-spin interactions triggers a new Hall effect that we coined the non-collinear Hall effect. We found that topological magnetic textures such as skyrmions carry a topological orbital moment that is not induced by the spin-orbit interaction but instead by the non-collinearity of the spin-texture. We proposed how to measure it with optical means. We also found that skyrmions interact with single atomic defect following a universal pattern dictated by the electronic filling of the electronic states of the defect. This allows us to predict how an atom will interact with skyrmions just by knowing its location in the periodic table. Atom-by-atom manufacturing of multi-atomic defects permits the breeding of their energy profiles. The resulting interaction phenotype is rich and unexpected. Moreover, we demonstrated that atomic defects can be utilised to trigger new highly-efficient modes of spin-mixing magnetoresistance (XMR), introduced previously by our group, enabling the all-electrical detection of non-collinear spin-textures.

We found a new contribution to the orbital magnetic moment, which can be as large as the atomic-like one accessible from standard DFT codes. In the context of spin-excitations, we found that even non-magnetic adatoms can carry excitations of paramagnetic natures, promoting the boring non-magnetic atoms to highly interesting objects for information nanotechnology. We discovered that the zero-bias anomalies known for Co-adatom originate from gaped spin-excitations induced by a finite magnetic anisotropy energy, in contrast to the usual widespread interpretation relating them to Kondo resonances. We also demonstrated that instead of the Kondo resonance, a new many-body state emerge from the interaction of electrons with spin-excitations, which we name spinaron. We furthermore unravelled the dynamical behaviour of Hall effects and have shown that the Hall angles, dynamical spin-orbit torques as well as various magnetoresistance effects get dramatically enhanced in the AC-regime. In nanoscale objects, it is expected that zero-point fluctuations will be important. We evaluated for the first time the zero-point spin-fluctuations and found that they can be as large as the magnetic moments. This has a dramatic impact on magnetic properties such as the magnetic anisotropy energy and the magnetic exchange interactions. We contributed to the establishment of a logical scheme for a four-state memory based on clusters made of three magnetic atoms deposited on a non-magnetic substrate and have shown how atomic manipulation can be utilized to suppress spin-fluctuations by nonlocally enhancing the spatial symmetry of the nanostructure.
We already made good progress beyond the state of the art. In the future we will continue to explore the new chiral magnetic interactions that we discovered. We plan to investigate antiferromagnetic skyrmions which host several advantages over the ferromagnetic ones. Initial investigations show that we are on the right track. The methodology for the evaluation of the interaction of the electron and spin-excitations in large non-collinear spin-textures is being completed. While we can currently access zero-point spin-fluctuations, we are aiming at improving the scheme allowing to evaluate their impact on the magnetic properties of not only sub-nanoscale nanostructures but also of large magnetic textures. We expect to continue exploring several ideas and projects that emerged from our proposal.
Frequency dependence of the AC charge currents on the magnetization's direction in Co/Pt(001)
Protocol for optical detection of topological orbital moments and topological charge of skyrmions
zero-point spin-fluctuations of a single atom deposited on a non-magnetic substrate
The interaction profile of a skyrmion with a neighbouring single-atomic defect
Theoretical proposal for spin-resolved electron energy-loss spectroscopy (SREELS)
Various Spin-waves in a skyrmion lattice as would be measured with electron energy loss spectroscopy